In 1573 “the Old Shore” of South Dublin continued to Townsend Street, then called Lazey or Lazar’s Hill (also Louseyhill, Louzy Hill and Lowsyhill) from the leper hospital. This is too far away to have any direct connection with Beggars Bush at Donnybrook.
I have encountered an article by Sean Donnelly which speculates that connects the two sites in Dublin through Poor Robin’s An Almanack of the old and new fashion (1694) which says “Since the King of the Beggars was married to the Queen of the Sluts at Lowzy-Hill near Beggars-Bush, being most splendidly attended by a ragged Regiment of Mumpers.” I do not believe this has anything to do with Dublin.

“Poor Robin” was the fictional author of a series of almanacs published from 1667 to 1756, the earliest editions of which have been attributed to William Winstanley of Quendon, near Saffron Waldon, Essex. The almanacs combined parody and trivia, real and fictional events, such as the birthdays of Mother Shipton, Doctor Faustus and Cardinal Richelieu. Lowzy (lousy) Hill in thos work is likely to be a fictional location, the louse being a symbol of beggars, along with the bush, staff and bag.

There is no reason to assume that the pamphlet, written in Essex and published in London, referred to an actual event in Dublin, for which no other record survives.

Poor Robin (1694) An almanack of the old and new fashion, or an ephemeris jestingly solid and jocosiously serious, wherein the reader may find (if he be endued with five degrees beyond the longitude of [J]ack Adam’s capacity) many remarkable things worthy his choicest observation
available on EEBO for those with access